Conjugate gradient preconditioned by regularization with Ritz postprocessing for ill-posed problems

Chabib, Ahmed

doi:10.1016/j.cma.2026.119104

Conjugate gradient preconditioned by regularization with Ritz postprocessing for ill-posed problems

2026-05-01

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DOI：10.1016/j.cma.2026.119104

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Abstract

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This paper proposes a conjugate gradient framework for Lavrentyev-regularized ill-posed problems in which the regularization operator is also used as the preconditioner. This choice provides meaningful norms for monitoring convergence and enables an efficient Ritz-based postprocessing of the iterates. In particular, approximate solutions associated with a whole range of regularization parameters can be obtained at negligible additional computational cost. The approach is assessed on a boundary data completion problem and on optical flow estimation, where it is used as the inner linear solver.

Keywords:

Regularization

Preconditioning

Conjugate gradient

Ritz values

L-curve

Picard plot

Conjugate gradient preconditioned by regularization with Ritz postprocessing for ill-posed problems

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